SPOJ - SUBLEX Lexicographical Substring Search

题目连接：

Description

Little Daniel loves to play with strings! He always finds different ways to have fun with strings! Knowing that, his friend Kinan decided to test his skills so he gave him a string S and asked him Q questions of the form:

If all distinct substrings of string S were sorted lexicographically, which one will be the K-th smallest?

After knowing the huge number of questions Kinan will ask, Daniel figured out that he can't do this alone. Daniel, of course, knows your exceptional programming skills, so he asked you to write him a program which given S will answer Kinan's questions.

Input

In the first line there is Kinan's string S (with length no more than 90000 characters). It contains only small letters of English alphabet. The second line contains a single integer Q (Q <= 500) , the number of questions Daniel will be asked. In the next Q lines a single integer K is given (0 < K < 2^31).

Output

Output consists of Q lines, the i-th contains a string which is the answer to the i-th asked question.

Sample Input

aaa
2
2
3

Sample Output

aa
aaa

Hint

题意

求一个字符串的所有字串中字典序第K的子串，相同子串只计算一次

题解：

先对后缀自动机dp，f[i]表示从节点i出发的不相同子串个数 $f[i] = 1 + \sum f[j]$
dp的过程中注意剪枝，如果f[i]已经计算过就不用往下dfs了，不然如果建出来的自动机是个菊花图，复杂度就会爆炸
最后在后缀自动机上dfs求出第k小子串就好了

代码

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int mx = 1e6+5;

struct SAM_automaton {
    int Next[mx][26], len[mx], fa[mx];
    int last, tot;
    int newnode() {
        tot++;
        for (int i = 0; i < 26; i++) Next[tot][i] = 0;
        return tot;
    }

    void init() {
        tot = 0;
        last = newnode();
    }

    void add(int c) {
        int p = last;
        int np = last = newnode();
        len[np] = len[p] + 1;
        while (p && !Next[p][c]) {
            Next[p][c] = np;
            p = fa[p];
        }
        if (!p) fa[np] = 1;
        else {
            int q = Next[p][c];
            if (len[q] == len[p] + 1) fa[np] = q;
            else {
                int nq = newnode();
                len[nq] = len[p] + 1;
                fa[nq] = fa[q];
                for (int i = 0; i < 26; i++) Next[nq][i] = Next[q][i];
                fa[q] = fa[np] = nq;
                while (p && Next[p][c] == q) {
                    Next[p][c] = nq;
                    p = fa[p];
                }
            }
        }
    }
}SAM;

char str[mx];
int r[mx], b[mx], id[mx], f[mx], ans[mx];

void dfs(int deep, int now, int tot) {
    if (--tot == 0) {
        for (int i = 1; i < deep; i++) putchar(ans[i]+'a');
        putchar('\n');
        return;
    }
    for (int i = 0; i < 26; i++) {
        int np = SAM.Next[now][i];
        if (np) {   
            if (tot > f[np]) tot -= f[np];
            else {            
                ans[deep] = i;
                return dfs(deep+1, np, tot);
            }
        }
    }
    
}

int build(int u) {
    if (f[u]) return f[u];
    f[u] = 1;
    for (int i = 0; i < 26; i++) {
        if (SAM.Next[u][i])
            f[u] += build(SAM.Next[u][i]);
    }
    return f[u];
}

int main() {
    SAM.init();
    scanf("%s", str);
    int len = strlen(str);
    for (int i = 0; i < len; i++) SAM.add(str[i] - 'a');
    build(1);

    int q;
    scanf("%d", &q);
    while (q--) {
        int tot;
        scanf("%d", &tot);
        dfs(1, 1, tot+1);
    }
    return 0;
}